Midfielder Fabian Delph put City ahead after 22 minutes, his speculative effort squirming under keeper Wayne Hennessey.
Aguero doubled the lead just before halftime when his shot from 30 metres hit defender Scott Dann's head and flew past the helpless Hennessey.
The Argentine struck again from close range after 68 minutes following a fine one-touch passing move and a perfect cross from Kevin De Bruyne before David Silva completed the rout.
Manchester City manager Manuel Pellegrini was pleased with his players after they briefly went back to the summit before Leicester City reclaimed top spot by one point with a 1-1 draw at Aston Villa in the late game.
"We had to refresh the team as we had less than 72 hours and that is not enough to recover," he told the BBC, referring to Wednesday's 0-0 draw with Everton.
"The first-half goals gave us more space as they (Palace) have had to go for the draw. That allowed us to use that space and score two more."
Palace manager Alan Pardew is planning to keep faith with Hennessey who also made a costly mistake in the 1-0 defeat at Aston Villa on Tuesday.
"Wayne is going to have to show me this week in training. A mistake at Villa, he needed to respond today and made another mistake," Pardew said.
"The ball is in his court to keep out the other two goalkeepers but I need to see it in training, I need to see a reaction from him. I will give him that chance because he deserves it."
(Reporting by Ed Osmond and Ian Chadband; editing by Clare Fallon)
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